There aren't two adjectives. The past participle "cleaned" is functioning as an adjective, while "deeply" is an adverb that's defining "cleaned." Participles are often used as adjectives. "a deeply cleaned room" = a room that has been deeply cleaned

Nothing is conjugated. There is no verb to conjugate. If you had written: "He cleaned the room deeply" then "cleaned" would be the past tense of "to clean". THAT is conjugation. Although "cleaned" in your sentence looks the same as the past tense of "to clean", appearances are deceiving. A past participle might sometimes look like a past tense, but it is not a verb and it is not conjugated.

"Deeply cleaned room" describes a room that has been cleaned (once, or recently). That room was not clean prior. Vs. "Deeply clean room" describes a room that is always clean.